Beetroot and cheese is a sandwich about a counterweight. Beetroot on its own is earthy and sweet and sharp with pickling vinegar, a single insistent register that gets tiring across a whole sandwich. Cheese is added not for richness but for salt: a firm, sharp cheese sets a savoury, fatty wall against the beetroot's sweetness so that each bite reads as contrast rather than as one sweet-sour note repeated. Take the cheese away and you have a beetroot sandwich, which is a different and narrower thing. The cheese is the reason this combination earned its own name.
The craft is balancing the counter while still managing the bleed beetroot always brings. The slices are drained well, because their crimson liquor will stain the bread and the cheese both if it is not removed first. A firm cheese, typically a mature Cheddar, is cut thick enough to hold its own against the beetroot and, usefully, doubles as part of the barrier: a solid slab of cheese laid against the crumb keeps some of the colour and moisture off the bread. Butter to the edges finishes the waterproofing and carries the cheese's salt across the slice. The bread is soft and plain so neither the earthy sweetness nor the sharp dairy is fought by an assertive crust. It is built cold and pressed lightly so the two layers settle into one without the beetroot weeping through.
The salt-against-sweet idea has obvious neighbours that work the same way with different proteins. Beetroot with egg leans on a milder, bound saltiness; with cold beef it sits inside a roast-leftover frame; with a crumbled blue it pushes the salt much harder. The plain beetroot sandwich is the version with the counterweight removed. Those deserve their own articles rather than being crowded in here.